Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy

TL;DR

This study applies detrended fluctuation analysis to compare correlation properties of Erdős-Rényi and scale-free networks under attack-repair strategies, revealing distinct scaling behaviors and correlation patterns.

Contribution

It introduces DFA to analyze network correlations under attack-repair, highlighting differences between random and scale-free networks in their fluctuation behaviors.

Findings

Maximum degree shows similar scaling in both networks.

Random graphs exhibit long-range power-law correlations.

Scale-free networks are uncorrelated at short scales and anticorrelated at long scales.

Abstract

We analyze the correlation properties of the Erdos-Renyi random graph (RG) and the Barabasi-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k_max, representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability p_re. The average degree <k>, revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of p_re.